Followup, with good news:
The Catalina VM I mentioned before (running in VMWare Fusion) is now connecting fine with the iLok.
The trick was in Fusion’s Virtual Machine Settings window, to open the USB & Bluetooth pane, and downgrade “USB Compatibility” from 3.1 to 2.0. This was mentioned above in a post in this thread, so thank you for the idea.
Full setup details for those who are troubleshooting:
Host system: macOS 10.14.6
VMware Fusion 11.5.6
VM OS: macOS 10.15.1
iLok is an iLok 2 (plastic casing)
PS: No changes to System Preferences > Security & Privacy > Full Disk Access were needed in this case.